JEE-Advanced 2015 (28/40)

Geometry Level 5

Suppose that p,q\vec p, \vec q and r\vec r are three non-coplanar vectors in R3\mathbb R^3. Let the components of a vector s\vec s along p,q\vec p, \vec q and r\vec r be 4, 3 and 5 respectively. If the components of this vector s\vec s along (p+q+r),(pq+r)(-\vec p+\vec q+\vec r),(\vec p- \vec q +\vec r) and (pq+r)(-\vec p -\vec q +\vec r) are x,yx,y and zz respectively, then find the value of 2x+y+z2x+y+z.

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